Nuprl Lemma : sq_stable__uall
∀[A:Type]. ∀[P:A ⟶ ℙ]. ((∀[x:A]. SqStable(P[x])) ⇒ SqStable(∀[x:A]. P[x]))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T
Lemmas referenced :
squash_wf,
uall_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
Error :universeIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
Error :functionIsType,
universeEquality,
independent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. ((\mforall{}[x:A]. SqStable(P[x])) {}\mRightarrow{} SqStable(\mforall{}[x:A]. P[x]))
Date html generated:
2019_06_20-AM-11_15_26
Last ObjectModification:
2018_09_26-AM-09_59_34
Theory : core_2
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